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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of the direct function and exponential function > Involving products of two direct functions and algebraic functions of exp > Involving (a+b ed z)beta cosh(e z)cosh(c z)





http://functions.wolfram.com/01.20.21.2798.01









  


  








Input Form





Integrate[(a + b E^(d z))^\[Beta] Cosh[e z] Cosh[c z], z] == ((1/4) (a + b E^(d z))^\[Beta] ((1/(c - e)) (E^((c - e) z) Hypergeometric2F1[(c - e)/d, -\[Beta], (c + d - e)/d, -((b E^(d z))/a)] - E^((-c + e) z) Hypergeometric2F1[(-c + e)/d, -\[Beta], (-c + d + e)/d, -((b E^(d z))/a)]) + (1/(c + e)) (E^((c + e) z) ((-E^(-2 (c + e) z)) Hypergeometric2F1[-((c + e)/d), -\[Beta], -((c - d + e)/d), -((b E^(d z))/a)] + Hypergeometric2F1[(c + e)/d, -\[Beta], (c + d + e)/d, -((b E^(d z))/a)]))))/ (1 + (b E^(d z))/a)^\[Beta]








Standard Form





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MathML Form







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</ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <ci> d </ci> <ci> e </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> c </ci> <ci> e </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <ci> e </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <ci> e </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <apply> <plus /> <ci> c </ci> <ci> d </ci> <ci> e </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <ci> c </ci> <ci> e </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <ci> e </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18